From most locations not nearby, you'll take Lake Shore Drive to the Museum of Science and Industry. Most highways feed in to Lake Shore, although often with a little trouble.
Taking Lake Shore Drive from the North
From many areas in the city, or from several highways around Chicago, you'll eventually end up heading south on Lake Shore Drive towards the museum. The high rises in Kenwood are a heads up that the museum will be coming up soon. Don't stay in the far right lane as it will split off twice near the high rises. If you're in the second lane to the right at that point and stay in that lane, that will continue and become the right lane after those exits. Stay in the right to exit at 57th Drive for the museum. Take a right at the stoplight (you'll see the museum in front of you as you do that). Stay in the left regular lane, but not the turn lane yet: the first stoplight has a turn lane that looks like it goes directly towards the front of the museum—that is just for taxis and busses. If you're parking, continue going straight and follow the curve to the left. You'll take a left at that light (E 57th Street), which will take you into the underground parking structure.
From the North or West (including Southwest or Northwest)
If you're coming in on I-94 from the north, I-90 from the northwest, I-290 from the west, or I-55 from the southwest, you'll eventually get to Lake Shore Drive which will take you to the museum. I-90 and I-94 merge as they approach the city, continue following those south. Likewise, from I-290 go east towards downtown and take the exit from the right lane to join I-90/94 south towards Indiana. From I-90/94, you'll take the exit for I-55 towards Lake Shore Drive, that will split into north and south options and you'll want north towards Lake Shore Drive. I-55 north will bring you to Lake Shore Drive and you'll keep on the right to go south on Lake Shore Drive. From there, follow the instructions above taking Lake Shore Drive.
From the East or South
If coming from the east on either the Skyway (I-90) or I-94, you'll take the same route. Take the Stony Island Ave exit from either (exit 103 from the Skyway, or exit 65 from I-94) and go north, following the signs to get to Lake Shore Drive (eventually taking a slight right onto Cornell Drive). You'll start seeing a park on your right and then the museum. The underground parking is a poorly marked right turn immediately after you pass a museum building—to the left will be E 57th Street, you'll turn right instead. (For a little more detail: you'll pass the lagoon on your right and see a surface lot on your as you come even with the main building; directly after that is a part of the building that's closer to the road, and you'll take a right immediately after that into the underground parking.)